simplify ln(6*10^5)

Solution

simplify

ln (6 \cdot 1 0^{5})

ln (6) + 5 ln (10)

Decimal Notation

13.30468 \dots

Solution steps

ln (6 \cdot 1 0^{5})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (6 \cdot 1 0^{5}) = ln (6) + ln (1 0^{5})

= ln (6) + ln (1 0^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{5}) = 5 ln (10)

= ln (6) + 5 ln (10)

80 ln (\frac{36185125}{289759})

ln ((1 + x)^{3} (2 x - 5)^{6})

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